N-dimensional geometries and Einstein equations from systems of PDE's

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/196933The aim of the present work is twofold: first, we show how all the $n$-dimensional Riemannian and Lorentzian metrics can be constructed from a certain class of systems of second-order PDE's which are in duality to the Hamilton-Jacobi equation and second we impose the Einstein equations to these PDE's.General Relativity and Quantum CosmologyN-dimensional geometries and Einstein equations from systems of PDE'stext